There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{(1 - {2}^{x})}{(1 + {2}^{x})}) + \frac{log_{3}^{1 - x}}{(1 + x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-{2}^{x}}{({2}^{x} + 1)} + \frac{log_{3}^{-x + 1}}{(x + 1)} + \frac{1}{({2}^{x} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-{2}^{x}}{({2}^{x} + 1)} + \frac{log_{3}^{-x + 1}}{(x + 1)} + \frac{1}{({2}^{x} + 1)}\right)}{dx}\\=&-(\frac{-(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + 0)}{({2}^{x} + 1)^{2}}){2}^{x} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{({2}^{x} + 1)} + (\frac{-(1 + 0)}{(x + 1)^{2}})log_{3}^{-x + 1} + \frac{(\frac{(\frac{(-1 + 0)}{(-x + 1)} - \frac{(0)log_{3}^{-x + 1}}{(3)})}{(ln(3))})}{(x + 1)} + (\frac{-(({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + 0)}{({2}^{x} + 1)^{2}})\\=&\frac{{2}^{(2x)}ln(2)}{({2}^{x} + 1)^{2}} - \frac{{2}^{x}ln(2)}{({2}^{x} + 1)} - \frac{log_{3}^{-x + 1}}{(x + 1)^{2}} - \frac{1}{(x + 1)(-x + 1)ln(3)} - \frac{{2}^{x}ln(2)}{({2}^{x} + 1)^{2}}\\ \end{split}\end{equation} \]

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